This study will test whether sirolimus can help patients with diabetic macular edema. The macula, the area of the retina that is responsible for fine vision, can become edematous due to diabetes and result in visual loss. Sirolimus inhibits a protein in the body called mTOR, which plays a critical role in regulating how cells divide and grow. Sirolimus is also believed to affect the inflammatory process. For both these reasons, the drug may be helpful in treating diabetic macular edema. This study is an open label pilot study of five participants with diabetic macular edema. After receiving a 20 L (440 g) subconjunctival injection in the study eye at baseline and Month 2, the participants will be re-evaluated every two months for at least one year for possible additional injections. During follow-up, participants will not undergo re-injection if they show significant clinical improvement or treatment success, defined as no intraretinal fluid or cysts present on optical coherence tomography (OCT) OR 100% reduction in excess retinal thickness over 260 microns on OCT OR no leakage on fluorescein angiography (FA). Beginning at Month 4, participants will be assessed for treatment failure, defined as loss of 15 or more letters of vision compared to baseline at two consecutive visits OR a 50% or greater increase in total retinal thickness as measured by OCT at two consecutive visits. Individual participants deemed treatment failures will continue receiving sirolimus injections, but will be allowed to receive focal laser therapy for any amenable leaking microaneurysms at Month 4. Beginning at Month 6, focal laser therapy will be permitted for both treatment failures and participants who do not meet the criteria of a treatment success. Participants will have the option of continuing treatment until a common termination date of one year. The primary outcome is the change in visual acuity in the study eye at six months compared to baseline. Secondary outcomes include changes in visual acuity in the study eye at one year as compared with baseline, changes in retinal thickness as measured by OCT and changes in fluid leakage in the macula as demonstrated by FA at six months, one year and throughout the study period in the study and fellow eyes. Safety outcomes include number and severity of systemic and ocular toxicities, adverse events and infections, and the number of participants withdrawn from study therapy.